How do I predict how a number will evolve based on its evolution in a short span?

Greetings,

First of all I am sorry if this has been posted before [I have tried searching] and/or if it seems like a beginner's question.
Now on with the question: Let's say we have a number X, we monitor it for 10 time units, in these 10 time units, the number changes value [based on user input] 6 times like so:

The number thus becoming X + 5 in a 10 time unit interval.
Based on this information, is it possible to predict how the number will evolve?
I am really interested in the theory behind this so if you could further direct me to information sources it would be great!